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JOURNALS // Vestnik Tomskogo Gosudarstvennogo Universiteta. Matematika i Mekhanika // Archive

Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2020 Number 68, Pages 33–40 (Mi vtgu812)

This article is cited in 1 paper

MATHEMATICS

On the set $K_{p}$ in finite groups

A. I. Zabarina, E. A. Fomina

Tomsk State Pedagogical University, Tomsk, Russian Federation

Abstract: The properties of the set $K_{p}$ consisting of elements of a non-Abelian group commuting with exactly $p$ elements of the group are considered. In particular, the properties of the set $K_{p}$ in permutation groups and some solvable groups. One more proof is given that all involutions of a finite simple non-Abelian group $G$ with a nonempty set $K_{3}$ form one conjugacy class.

Keywords: group, centralizer of an element, involution, Sylow and Hall subgroups.

UDC: 512.543

MSC: 20D99

Received: 14.04.2020

DOI: 10.17223/19988621/68/3



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